roicca IN DIFTEREXT PLAXE*. ; 



; ic finit nart of the investigation 

 imposition to establish thai the fora* - 



Or we may resolve the force* at right angles to a foe 

 instead of parallel to an edge, and thus obtain the ranlt 



reaolve the forces at right angles to the foe 7 

 we have one force represented by the area BCD, and the 

 resolved parts of the other forces are represented by the pro- 

 jections of the respective areas RAO, CAD, DAB on J 



sura of these projections is equal to In '/>. Thus 

 the forces resolved at right angles to BCD vanish. 



' y the forces resolved at right angles to any other 



fmv 



III. By a process similar to that used in nstshlSshisj 



v. we can extcn 



preceding Proposi: -lie case of any polyhedron bounded 



iangular faces. Thus we obtain the following remit : 



a polyhedron bounded by triangular foes at 



angles to the faces and proportional to their areas, the 



points of applicn: TCCS being the centres < 



i Bribing the faces ; shew that if the forces all act 

 inwards or all act outwards they will be in equilibria 



ces acting on a rigid body are in equi- 

 librium, and a tetrahedron be constructed by drawing pimps 

 .cht angles to the directions of the forces, the forces 

 will bo respectively proportional to the areas of the foes* 



converse of n. and may be readily demon- 



1: for by resolving the forces in any direction, and 



- the areas on a plane at right angles to that dircc- 



that th roes are connected by the same 



as the four areas* 



om this result that the areas in the prtsiSJt 



theorem must be respectively proportional to the volumes 

 ii-reil in tin* Proposition X. at thc^ end o: 

 ctly arrive at a 



